This is the third edition of the classic textbook on the subject. With its clear writing, strong organization, and comprehensive coverage of essential theory it is like a personal guide through this important topic, and now has lots of extra material.

This is the third edition of the classic textbook on the subject, and it is even more relevant to students of, and researchers in, mathematics than ever before. With its clear writing, strong organization, and comprehensive coverage of essential theory it is like a personal guide through this important topic. The book contains proofs of important results and the representation of key algorithms in a Pascal-like notation that allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises provide a rich seam of material for self-study by students. This new edition contains additional material including two new application sections (on graphical codes and their decoding) and a number of extra exercises (with solutions, as throughout the text). What's more, recent developments have been discussed and referenced, in particular for the traveling salesman problem.

Includes supplementary material: sn.pub/extras

Autorentext

Dirk Hachenberger is a mathematician working in the fields of combinatorics, number theory, applicable algebra, finite geometry and coding theory. He is the recipient of the 2004 Hall medal of the Institute for Combinatorics and its Applications (ICA). He was also awarded the price for good teaching of the Bavarian State Minister for Science, Research and Arts in 2004. He has published the books "Finite Fields: Normal bases and completely free elements" (in English) and "Mathematics for computer scientists" (in German). Dieter Jungnickel is an internationally known mathematician working in the fields of applicable algebra, coding theory, design theory, finite geometry, combinatorics and combinatorial optimization. He is the recipient of the 2018 Euler medal of the Institute for Combinatorics and its Applications (ICA). He has published several well-known books, including "Design Theory", "Optimization Methods", "Finite fields: Structure and arithmetics", "CodingTheory", "Combinatorics" and "Graphs, Networks and Algorithms", some of which have been published both in English and German.

Klappentext

From the reviews of the previous editions

".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..."

K.Engel, Mathematical Reviews 2002

The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended.

P .B. Gibbons, Zentralblatt für Mathematik 1061, 2005

The third edition of this standard textbook contains additional material: two new application sections (on graphical codes and their decoding) and about two dozen further exercises (with solutions, as throughout the text). Moreover, recent developments have been discussed and referenced, in particular for the travelling salesman problem. The presentation has been improved in many places (for instance, in the chapters on shortest paths and on colorings), and a number of proofs have been reorganized, making them more precise or moretransparent.

Inhalt
Basic Graph Theory.- Algorithms and Complexity.- Shortest Paths.- Spanning Trees.- The Greedy Algorithm.- Flows.- Combinatorial Applications.- Connectivity and Depth First Search.- Colorings.- Circulations.- The Network Simplex Algorithm.- Synthesis of Networks.- Matchings.- Weighted matchings.- A Hard Problem: The TSP.